A singular Riemannian geometry approach to Deep Neural Networks I. Theoretical foundations

Alessandro Benfenati, Alessio Marta

Abstract: Highlights•We consider Neural Networks as sequences of smooth maps between manifolds.•We investigate the structures induced through pull-backs on the manifolds.•The pull-backs of the final Riemannian metric to any manifolds is a degenerate metric.•The theoretical study leads to construct equivalence classes in the input manifold.